Numerical Errors

2018 ◽  
pp. 1-5
Author(s):  
George Rawitscher ◽  
Victo dos Santos Filho ◽  
Thiago Carvalho Peixoto
Keyword(s):  
Numerical Errors

Current status of special planetary and lunar theories and ephemerides

1966 ◽  
Vol 25 ◽  
pp. 266-267
Author(s):  
R. L. Duncombe
Keyword(s):  
Observational Data ◽  
Current Status ◽  
Numerical Errors

An examination of some specialized lunar and planetary ephemerides has revealed inconsistencies in the adopted planetary masses, the presence of non-gravitational terms, and some outright numerical errors. They should be considered of temporary usefulness only, subject to subsequent amendment as required for the interpretation of observational data.

scholarly journals The Model Order Reduction Method as an Effective Way to Implement GPC Controller for Multidimensional Objects

Algorithms ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 178
Author(s):  
Sebastian Plamowski ◽  
Richard W Kephart
Keyword(s):  
Predictive Control ◽  
Model Order Reduction ◽  
Order Reduction ◽  
High Order ◽  
Double Precision ◽  
Model Order ◽  
Numerical Errors ◽  
Multiple Input ◽  
Multidimensional Objects ◽  
Order Reduction Method

The paper addresses issues associated with implementing GPC controllers in systems with multiple input signals. Depending on the method of identification, the resulting models may be of a high order and when applied to a control/regulation law, may result in numerical errors due to the limitations of representing values in double-precision floating point numbers. This phenomenon is to be avoided, because even if the model is correct, the resulting numerical errors will lead to poor control performance. An effective way to identify, and at the same time eliminate, this unfavorable feature is to reduce the model order. A method of model order reduction is presented in this paper that effectively mitigates these issues. In this paper, the Generalized Predictive Control (GPC) algorithm is presented, followed by a discussion of the conditions that result in high order models. Examples are included where the discussed problem is demonstrated along with the subsequent results after the reduction. The obtained results and formulated conclusions are valuable for industry practitioners who implement a predictive control in industry.

A numerical approach for structural system identification by observability techniques

2016 ◽  
Author(s):  
Jose Antonio Lozano Galant ◽  
Maria Nogal ◽  
Jun Lei ◽  
Dong Xu ◽  
José Turmo
Keyword(s):  
System Identification ◽  
Numerical Approach ◽  
Mathematical Foundation ◽  
Structural System ◽  
Numerical Errors ◽  
Definition Of ◽  
Structural System Identification ◽  
Symbolic Approach

Observability techniques enable the structural system identification of static structures from a symbolic approach. The main advantage of this method is its deep mathematical foundation that enables the definition of parametric equations for the estimates. Nevertheless, this symbolic approach is not enough for the application of this method on actual structures. To fill this gap, this article presents the introduction into the symbolic structural system identification by observability techniques of a new numerical approach. This application includes the development of an algorithm that reduces the unavoidable numerical errors produced by the lack of precision of computers. The comparison of the observability technique with other existing methods presented in the literature shows that the number of required measurements is significantly lower. Furthermore, contrary to other analysed methods, no information from the undamaged structure is required.

The Physical and Computer Modeling of Plastic Deformation of Low Carbon Steel in Semisolid State

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Marcin Hojny ◽  
Miroslaw Glowacki
Keyword(s):  
Computer Simulation ◽  
Low Carbon Steel ◽  
Mass Conservation ◽  
Analytical Form ◽  
Plastic Behavior ◽  
Volume Loss ◽  
Low Carbon ◽  
Compression Tests ◽  
Thermomechanical Model ◽  
Numerical Errors

This paper reports the results of theoretical and experimental work leading to the construction of a dedicated finite element method (FEM) system allowing the computer simulation of physical phenomena accompanying the steel sample testing at temperatures that are characteristic for integrated casting and rolling of steel processes, which was equipped with graphical, database oriented pre- and postprocessing. The kernel of the system is a numerical FEM solver based on a coupled thermomechanical model with changing density and mass conservation condition given in analytical form. The system was also equipped with an inverse analysis module having crucial significance for interpretation of results of compression tests at temperatures close to the solidus level. One of the advantages of the solution is the negligible volume loss of the deformation zone due to the analytical form of mass conservation conditions. This prevents FEM variational solution from unintentional specimen volume loss caused by numerical errors, which is inevitable in cases where the condition is written in its numerical form. It is very important for the computer simulation of deformation processes to be running at temperatures characteristic of the last stage of solidification. The still existing density change in mushy steel causes volume changes comparable to those caused by numerical errors. This paper reports work concerning the adaptation of the model to simulation of plastic behavior of axial-symmetrical steel samples subjected to compression at temperature levels higher than 1400°C. The emphasis is placed on the computer aided testing procedure leading to the determination of mechanical properties of steels at temperatures that are very close to the solidus line. Example results of computer simulation using the developed system are presented as well.

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